Confidence Intervals for One Sample Proportion
Microsoft takes a random sample of 300 employees and finds that 120 work in Excel daily. Find a 95% CI for the proportion of Microsoft workers who use Excel daily.
(0.345,0.455)
Vons runs a study on their floral products. They collect a random sample of 400 bouquets and find a 95% CI for the mean number of flowers in a bouquet to be (14, 23). Give an interpretation of this confidence interval.
We are 95% confident that the true mean number of flowers in a Vons bouquet is between 14 and 23 flowers.
Oaks Christian creates a 95% Confidence Interval for the proportion of students who play sports. They obtain the interval (0.68, 0.82). Interpret this confidence interval in context.
We are 95% confident that the true proportion of Oaks Christian students who play sports is between 0.68 and 0.82.
A coach wants to learn more about runners in elevated cities across the US. He randomly selects 50 runners from elevated cities in the US and finds they have a mean mile time of 7 minutes with a standard deviation of 1.5 minutes. Find a 95% CI for the mean mile time of runners in elevated cities in the US.
(6.58,7.42)
The NBA calculates a 95% CI for the proportion of players above 6ft 5in. The interval they produce is (0.54, 0.79). Explain whether this interval supports or goes against the claim "The majority of NBA players are taller than 6ft. 5in."
Supports: Since all of the confidence interval is above 0.5, it is likely that the true proportion is above 50% and thus a majority of NBA players are taller.
While learning more about ChatGPT usage at his high school, a student takes a sample of 40 people from his History class. He finds that his classmates use Chat on a mean of 8 assignments per week with a standard deviation of 1. Find a 95% CI for the mean number of assignments completed using ChatGPT if applicable.
Not applicable, sampling is not random :(
The Ronald Reagan Library is conducting a study on its visitors. They want to determine what proportion of visitors are international tourists. Out of a random sample of 400 visitors, they found 9 were from out of the country. Construct a 95% CI if applicable.
Not Applicable, fails Large Counts Condition. (400*9/400)=9<10.
A man claims that a 95% CI for the mean weight of Bichon Poodles is (11, 19). You weigh two random Bichon Poodles and find they both don't fall into the interval. What might this tell us about the man's CI?
It likely violated one (or more) of the three conditions:
1. Sample not random
2. Sample was more than 10% of all Bichon Poodles (unlikely).
3. Sample was less than 30 (didn't meet CLT).
Wildlife Biologists want to learn how rare are the jellyfish known as Turritopsis dohrnii (Or Immortal Jellyfish), which is capable of reverting from an adult to a polyp stage (thus making it "biologically immortal"). They sample 1000 random known jellyfish habitats and find that 15 of them have Immortal Jellyfish. Find and interpret a 95% CI for the proportion of jellyfish habitats that have an Immortal Jellyfish.
(0.0075, 0.0225)
Interpretation: We are 95% confident that the true proportion of jellyfish habitats that have a Immortal Jellyfish is between 0.0075 and 0.0225.
Staples Center is deciding on selling a bobblehead during Laker games. They give a random poll out to 2000 attendees asking how much they would pay for a Lebron bobblehead. They found the mean of the reported amounts to be $28 with a standard deviation of $2.75. Find and Interpret a 95% CI for the mean of the reported amounts customers would be willing to pay for a Lebron bobblehead.
(27.88, 28.12)
Interpretation: We are 95% confident that the true mean reported amount a customer would pay for a Lebron bobblehead is between $27.88 and $28.12.